Results 31 to 40 of about 54,142 (287)
Global Attractor for the Generalized Dissipative KDV Equation with Nonlinearity
International Journal of Mathematics and Mathematical Sciences, 2011 We discuss global attractor for the generalized dissipative KDV equation with nonlinearity under the initial condition u(x,0)=u0(x). We prove existence of a global attractor in space H2(Ω), by using decomposition method with cut-off function and ...
Zai-yun Zhang, Zhen-hai Liu
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On an exponential attractor for a class of PDEs with degenerate diffusion and chemotaxis [PDF]
, 2017 In this article we deal with a class of strongly coupled parabolic systems that encompasses two different effects: degenerate diffusion and chemotaxis.
A. Eden +30 more
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Embedding of global attractors and their dynamics [PDF]
, 2010 Using shape theory and the concept of cellularity, we show that if $A$ is the global attractor associated with a dissipative partial differential equation in a real Hilbert space $H$ and the set $A-A$ has finite Assouad dimension $d$, then there is an ...
de Moura, Eleonora Pinto +2 more
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Global Attractor for Sectorial Evolutionary Equation
Journal of Differential Equations, 1996 Let \(A\) be a sectorial operator with compact resolvent in an appropriate Banach space and consider the evolution equation \(\dot u + Au = F(u)\), \(t > 0\), \(u(0) = u_0\). The authors show that this problem generates a dissipative semigroup whenever an appropriate introductory estimate for solutions is known.
Cholewa, Jan W., Dlotko, Tomasz
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A non-autonomous scalar one-dimensional dissipative parabolic problem: The description of the dynamics [PDF]
, 2018 The purpose of this paper is to give a characterization of the structure of non-autonomous attractors of the problem $u_t= u_{xx} + \lambda u - \beta(t)u^3$ when the parameter $\lambda > 0$ varies.
Broche, Rita de Cássia D. S. +2 more
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Global attractors for p-Laplacian equation
Journal of Mathematical Analysis and Applications, 2007 The existence of a global attractor for the following \(p\)-Laplacian equation: \[ u_t-\text{div}\bigl(|\nabla u|^{p-2}\nabla u\bigr)+f(u)=g \quad\text{in } \Omega\times\mathbb{R}^+,\tag{1} \] with the Dirichlet boundary condition \[ u |_{\partial\Omega}=0\tag{2} \] and initial condition \[ u(x,0)=u_0(x)\tag{3} \] is proved in \(W_0^{1,p}(\Omega)\) and
Yang, Meihua +2 more
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Existence and attractors of solutions for nonlinear parabolic systems
Electronic Journal of Qualitative Theory of Differential Equations, 2001 We prove existence and asymptotic behaviour results for weak solutions of a mixed problem (S). We also obtain the existence of the global attractor and the regularity for this attractor in $\left[H^{2}(\Omega )\right] ^{2}$ and we derive estimates of its
Hamid El Ouardi, Abderrahmane El Hachimi
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Dynamic of the nonclassical diffusion equation with memory
Boundary Value Problems, 2023 In this paper, we consider the nonclassical diffusion equation with memory and the nonlinearity of the polynomial growth condition of arbitrary order in the time-dependent space.
Jing Wang +3 more
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Direct transition to high-dimensional chaos through a global bifurcation [PDF]
, 2005 In the present work we report on a genuine route by which a high-dimensional (with d>4) chaotic attractor is created directly, i.e., without a low-dimensional chaotic attractor as an intermediate step.
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Stability of limit regimes in general reaction-diffusion type systems
Науковий вісник Ужгородського університету. Серія: Математика і інформатика, 2022 In this paper, we consider the stability of limit regimes for a general class of nonlinear distributed mathematical models named Reaction-Diffusion models. RD systems naturally arise in many applications.
О. В. Капустян +1 more
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